On a Hybrid Fourth Moment Involving the Riemann Zeta-Function

Aleksandar Ivić () and Wenguang Zhai ()
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Aleksandar Ivić: Katedra Matematike RGF-a Universiteta u Beogradu
Wenguang Zhai: China University of Mining and Technology

A chapter in Topics in Mathematical Analysis and Applications, 2014, pp 461-482 from Springer

Abstract: Abstract For each integer 1 ≤ j ≤ 6, we provide explicit ranges for σ for which the asymptotic formula ∫ 0 T ζ 1 2 + i t 4 | ζ ( σ + i t ) | 2 j d t ∼ T ∑ k = 0 4 a k , j ( σ ) log k T $$\displaystyle{\int _{0}^{T}\left \vert \zeta \left (\frac{1} {2} + it\right )\right \vert ^{4}\vert \zeta (\sigma +it)\vert ^{2j}dt \sim T\sum _{ k=0}^{4}a_{ k,j}(\sigma )\log ^{k}T}$$ holds as T → ∞, where ζ(s) is the Riemann zeta-function. The obtained ranges improve on an earlier result of the authors. An application to a weighted divisor problem is also given.

Keywords: Riemann zeta-function; Hybrid moments; Exponent pairs; Asymptotic formula (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-06554-0_19

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